Question

Cole weighs 145 lb on the surface of the Earth. Cole travels to an exoplanet discovered recently. This exoplanet orbits a star that is 2.5 times as massive as our Sun. The planet itself is 0.40 times as massive as the Earth, and its diameter is half the diameter of the Earth. How many pounds will Cole weigh on the surface of this planet?

Answer 1

Solution:

Let us go to the basics first.

We know that Acceleration due to gravity of earth, g = 9.8 m/s² = GM_e / R_e².......................Eqn.1

[where, G = Gravitational constant; M_e = mass of earth; R_e = Radius of earth]

Given:

W = 145 lb

M_p = 0.40 * M_e

D_p = 0.5D_e

=>R_p = 0.5R_e

Thus, similarly as eqn.1, acceleration due to fravity of planet is given by:

a = GM_p / R_p² .......................Eqn.2

Performing Eqn2 divided by Eqn.1

a / g = (GM_p / R_p²) / (GM_e / R_e²)

=> a / g = (M_p / R_p²) / (M_e / R_e²)

=> a / g = [0.40 * M_e / (0.5R_e)²] / [M_e / R_e²]

=> a / g = [0.40 / (0.5)²]

=> a / g = 1.6

Thus, acceleration due to gravity on planet's surface is 1.6 times greater than that of earth.

As we know that weight of an object is proportional to the acceleration due to gravity.

So, weight of Cole on the surface of this planet = 1.6*145 lb = 232 lb (Answer)

Thanks!!!